[leftmargin=10pt]
ST-GB (Single Task GBDT)
trains a GBDT model for each task separately.

GBDT (Sec. ) trains a GBDT model on the whole dataset of all tasks.

MT-ET (Multi-Task ExtraTrees) [1]} is a tree-based ensemble multi-task learning method based on Extremely Randomized Trees.

MT-TNR [2]} is a linear MTL model with Trace Norm Regularization.

MT-B (Multi-Task Boosting) [3]} is an MTL algorithm with boosted trees. It trains task-common forest \(F_0\)  on all tasks, and trains task-specific boosted forest \(F_t,i\in \lbrace 1,2,...,T\rbrace \)  on each task separately. The final output of sample \(\mathbf {x}\)  of task \(t\)  is \(F_0(\mathbf {x})+F_t(\mathbf {x})\) .

CMTL [4]} is a clustered MTL method that assumes the tasks may exhibit a more sophisticated group structure.

TSGB\(_{\lambda }\) is a variant of TSGB proposed by us. Instead of using a threshold \(R\) , it decides whether to conduct a task-wise split with a fixed probability \(\lambda \in [0, 1]\) . TSGB\(_{\lambda }\)  picks a node with a certain probability and sort the tasks, then split the samples task-wisely as how TSGB do.

TSGB is the novel method proposed in this paper. It decides whether to perform a task-wise split by comparing a threshold ratio \(R\)  with the negative task gain ratio \(R_{\text{neg}}\)  of the current node. Then it separates samples task-wisely according to the positive and negative of their task gains.

